While packing for a business trip Mr. Debashis has packed 3 pairs of shoes, 4 pants, 3 half-pants,6 shirts, 3 sweater and 2 jackets. The outfit is defined as consisting of a pair of shoes, a choice of “lower wear” (either a pant or a half-pant), a choice of “upper wear” (it could be a shirt or a sweater or both) and finally he may or may not choose to wear a jacket. How many different outfits are possible ?
a) 567
b) 1821
c) 743
d) 1701

Answer: d
Explanation: Number of ways a pair of shoes can be selected,
= ³C₁
= 3 ways
Number of ways lower wear can be selected = (3 + 4) = 7 ways.
Number of ways upper wear can be selected, = 3 + 6 + (3 × 6)
= 27 ways
Number of ways jacket can be chosen or not chosen = 3 ways {No jacket, 1^st jacket, 2^nd jacket}.
Total number of different outfits
= 3 × 7 × 27 × 3
= 1701 ways